We consider the dynamics of a non-viscous incompressible fluid on a compact Riemannian manifold
of dimension two. We follow the treatments in [1]}, [2]}, [3]}
in the respects of treating the fluid velocity field as a one-form and in extensively using the Lie derivative.
These sources also provide the standard notions and notations for differential geometry to be used.
Other treatises in fluid dynamics, suitable for our purposes, are [4]}, [5]}.
